Help with this calculus problem.

  • Context: MHB 
  • Thread starter Thread starter JWelford
  • Start date Start date
  • Tags Tags
    Calculus
Click For Summary
SUMMARY

The integral \[\int_{-\infty}^{-0.4088}e^{-u^2/2} \,du\] does not possess an elementary antiderivative, making the application of the Fundamental Theorem of Calculus infeasible. The recommended approach is to evaluate this integral numerically. This integral is closely associated with standard normal distribution tables, and by multiplying the expression by \(1/\sqrt{2\pi}\), it can be transformed into a standard form suitable for lookup in these tables.

PREREQUISITES
  • Understanding of integral calculus and numerical integration techniques.
  • Familiarity with the Fundamental Theorem of Calculus.
  • Knowledge of standard normal distribution and its properties.
  • Experience with statistical tables or software for numerical evaluation.
NEXT STEPS
  • Learn numerical integration methods such as Simpson's Rule or Trapezoidal Rule.
  • Study the properties of the standard normal distribution and its applications.
  • Explore software tools like MATLAB or Python's SciPy for numerical evaluations of integrals.
  • Review how to use standard normal tables effectively for statistical calculations.
USEFUL FOR

Students and professionals in mathematics, statistics, and engineering who require assistance with calculus problems, particularly those involving non-elementary integrals and numerical methods.

JWelford
Messages
3
Reaction score
0
\[\int_{-\infty}^{-0.4088}e^{-u^2/2} \,du\]

Sorry i just can't seem to get these equations to actually display properly
 
Last edited:
Physics news on Phys.org
This integral does not have an elementary antiderivative, which means the Fundamental Theorem of the Calculus is not available to you. You're best off doing it numerically. This integral is highly related to standard normal tables (it's not quite there, but you could multiply by a $1/\sqrt{2\pi}$ to get it into a standard form). Then just look the value up in a table.
 

Similar threads

MHB Help With Integration Calculation - Struggling?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Having trouble understanding a seemingly simple u-substitution
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Why does the integral of sine of x^2 from - infinity to + infinity diverge?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Reasoning behind Infinitesimal multiplication
  • · Replies 22 ·
Replies
22
Views
4K
Undergrad Integrating a product of exponential and trigonometric functions
  • · Replies 21 ·
Replies
21
Views
4K
Undergrad Gaussian integral by differentiating under the integral sign
  • · Replies 19 ·
Replies
19
Views
4K
Undergrad The Vector Laplacian: Understanding the Third Term
  • · Replies 6 ·
Replies
6
Views
3K
MHB Integral of Rational Exponential
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Inequality with integral and max of derivative
  • · Replies 3 ·
Replies
3
Views
2K
MHB How do you solve this calculus 2 integration problem?
  • · Replies 13 ·
Replies
13
Views
3K